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National Cleaner Corp.needs a $1.5 million loan to finance a project that pays off next period.There are two projects available, A and B.You are a lending officer and know about the projects but cannot control the borrower's project choice.A will yield a payoff of $6.75 million with probability 0.6 or zero with probability 0.4.B will pay off $8 million with probability 0.5 or zero with probability 0.5.Everybody is risk neutral and the riskless interest rate is 10%.You consider designing a loan contract that involves the use of collateral However, collateral is costly and $1 of the borrower's collateral is worth only 90 cents to your bank.
-Suppose a secured loan is offered.How much collateral should you ask the borrower round to the nearest decimals)?
A)$1.41 million
B)$1.23 million
C)$0.87 million
D)$0.65 million
E)$0.50 million

Question

Use the following information for questions 
National Cleaner Corp.needs a $1.5 million loan to finance a project that pays off next period.There are two projects available, A and B.You are a lending officer and know about the projects but cannot control the borrower's project choice.A will yield a payoff of $6.75 million with probability 0.6 or zero with probability 0.4.B will pay off $8 million with probability 0.5 or zero with probability 0.5.Everybody is risk neutral and the riskless interest rate is 10%.You consider designing a loan contract that involves the use of collateral However, collateral is costly and $1 of the borrower's collateral is worth only 90 cents to your bank.
-Suppose a secured loan is offered.How much collateral should you ask the borrower round to the nearest decimals)?
A)$1.41 million
B)$1.23 million
C)$0.87 million
D)$0.65 million
E)$0.50 million

Quizplus · Accepted Answer

To determine the amount of collateral needed, we first calculate the expected payoff of the safer project (A) since the bank would prefer to ensure its loan is repaid and thus would base the collateral requirement on the project with the lower risk. The expected payoff for Project A is: (0.6 * $6.75 million) + (0.4 * $0) = $4.05 million. The loan amount is $1.5 million, and with a 10% interest rate, the bank expects to be repaid $1.65 million ($1.5 million * 1.10). Given that collateral is worth only 90 cents on the dollar to the bank, to secure the repayment of $1.65 million, the bank would need collateral worth $1.65 million / 0.9 = $1.833 million. However, since the expected payoff of Project A is only $4.05 million, the maximum collateral that can be realistically demanded (without making the project unattractive to the borrower) would be based on ensuring the bank can recover its $1.65 million if the project fails. The closest option provided that is less than the expected payoff and covers the loan repayment amount when considering the devaluation of collateral is $1.41 million. This ensures the bank can recover its funds while acknowledging the reduced value of collateral.

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